Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
The Machete Number, David Freund
The Machete Number, David Freund
Senior Independent Study Theses
Knot theory is a branch of topology that deals with the structure and properties of links. Employing a variety of tools, including surfaces, graph theory, and polynomials, we develop and explore classical link invariants. From this foundation, we de fine two novel link invariants, braid height and machete number, and investigate their properties and connection to classical invariants.
Let's Get In The Mood: An Exploration Of Data Mining Techniques To Predict Mood Based On Musical Properties Of Songs, Sarah Smith-Polderman
Let's Get In The Mood: An Exploration Of Data Mining Techniques To Predict Mood Based On Musical Properties Of Songs, Sarah Smith-Polderman
Senior Independent Study Theses
This thesis explores the possibility of predicting the mood a song will evoke in a person based on certain musical properties that the song exhibits. First, I introduce the topic of data mining and establish its significant relevance in this day and age. Next, I explore the several tasks that data mining can accomplish, and I identify classification and clustering as the two most relevant tasks for mood prediction based on musical properties of songs. Chapter 3 introduces in detail two specific classification techniques: Naive Bayes Classification and k-Nearest Neighbor Classification. Similarly, Chapter 4 introduces two specific clustering techniques: …
The Truth About Lie Symmetries: Solving Differential Equations With Symmetry Methods, Ruth A. Steinhour
The Truth About Lie Symmetries: Solving Differential Equations With Symmetry Methods, Ruth A. Steinhour
Senior Independent Study Theses
Differential equations are vitally important in numerous scientific fields. Oftentimes, they are quite challenging to solve. This Independent Study examines one method for solving differential equations. Norwegian mathematician Sophus Lie developed this method, which uses groups of symmetries, called Lie groups. These symmetries map one solution curve to another. They can be used to determine a canonical coordinate system for a given differential equation. Writing the differential equation in terms of a different coordinate system can make the equation simpler to solve. This I.S. explores techniques for finding a canonical coordinate system and using it to solve a given differential …